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A typology of systems and processes. A possible approach to the problem of complexity and emergence.

Dietrich Fliedner, Saarbruecken (Germany). University of the Saarland, Dept. of Geography

Abstract:

Depending on viewpoint, our reality consists of1. solid bodies ("solida") and "movements",2. self ordering "equilibrium systems" and "movement projects",3. self regulating "flow equilibrium systems" and "flow processes",4. self organizing "non-equilibrium systems" and "conversion processes",5. structurally self creating "hierarchy systems" and "hierarchical processes",6. a materially self creating "universal system" and "universal process".The autonomy of the systems increases with growing complexity. The "emergence processes" show the way from the simple to the complex. They always follow(geometrically) the same pattern, i.e. in accordance with a certain code, the flows are 1st bundled(bundling), 2nd positioned in the next higher level (alignment), 3rd interlaced with each other(interlacement), and 4th folded (folding). About the emergence processes cf. Appendix.

First published in September 1999:<http://www.uni-saarland.de/~d.fliedner/InterJournal/WASKOME7.html>Unchanged (except mistakes in writing)

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Introduction

There have been many attempts to describe and explain complexity (Lissack 1999). But whatexactly happens when complexity begins to emerge is still not understood. Perhaps thephenomenon may become clearer when we approach it via the structure of systems. This will beattempted in the following article.

The term "system" is derived from the Greek "συστηµα" which originates in turn from the verb"συνιστηµι" and therefore means something which is "an unified whole which is assembledfrom several parts". The term "complexity" has its roots in the greek "πλεκω", which means "toweave or tie together", and in the latin "complico", which means "to fold or wind together", i.e.more or less linear shaped objects are connected with and arranged around one another in sucha way that they yield something coherent which we can study in detail and as a whole.

Thus, both terms "system" and "complexity" refer to one another. Assembling, uniting, weaving,folding are processes which are controlled by information. Research into systems and complexityis therefore closely connected with research into information. Information positions matter andflows of energy, assigns them to one another, links them to one another, arranges them insequences to form processes, creates patterns, thereby allowing controlled distribution.

We will attempt now to define the various possibilities of coexistence between the componentsof systems according to the various degrees of complexity. In doing this, we will establish thearchetypes of the systems in order to arrive at an intrinsically consistent and complete typology.Any place in the Universe belongs to all types of systems simultaneously.

Our considerations are founded on the development of a theory of emergence which complexityand process sequence (from the point of view of the social sciences) link with one another. Eachsystem type is raised to the next more complex type by a process of emergence. It carries out theprocess, i.e. the development of new structural characteristics of a system which cannot beexplained by the elements alone. All system types are altered in basically the same way whenthey move up one level in the scale of complexity (cf. Appendix). The following four operationsare required [explained using the example of a blacksmith's forge, which emerges from a groupof farms]:

1. Bundling: A group of systems of a lower degreee of complexity come together in order to forma system of greater complexity. This accumulation of systems similar in structure and contentis termed "bundling". [E.g. farms are animated to supply the market with more products, i.e. to increase theirperformance. This causes an overload in work and prompts them to remove the labor-intensivesmithy work from the range of their activities. In the bundling stage, these individual activitiesare treated as a single whole.]

2. Alignment: These activities are arranged into a new whole, i.e. "aligned". This overridingprocess ("main process") is made up of 4 phases ("adoption" of the demand, "production" of thesupply, "reception" of the necessity to adapt the system itself, and "reproduction", i.e. thecorresponding change to the system). This can be depicted by a comprehensive system ofcoordinates (1st rank) which symbolizes the basic structure of the operations. In addition (the

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sum of the) systems with their own processes must be considered. All of them are subordinateto the new whole and involved in its processes. This can be represented by 2nd rank coordinatesystems which are inserted in each quadrant of the overriding (1st ranking) system. [Here the division of labor for the various types of blacksmith's work begins, the decision toparticipate in a common production process. The main process includes the satisfaction of thedemand for forged products and self-maintenance. In addition, the two segments planning andexecution.]

3. Interlacement: The individual processes now have to be incorporated in the main process. Tothis end, the existing process sequences are woven into the higher level of complexity. Theseprocesses take place perpendicularly to the previous ones, because this no longer concerns themany individual process sequences, but their organization into a whole. It takes place in aprocess resembling weaving, as described above. Mathematically, this involves a reversal of thecoordinate system.[Cooperation is intensified, the blacksmith's work is more strongly coordinated because not onlythe individual main stages are arranged in order, but the individual activities are brought togetheror woven into the main stages of the system. The workers involved therefore coordinate theiractions with one another in great detail.] 4. Folding: The system must appear as a unit to the outside world or to its environment. Themarket demanding the products appears as the ("superordinate" or) "superior environment" andthe market supplying the resources the ("subordinate" or "inferior environment". The beginningand the end of the main process are joined to one another by means of "folding". In this way, theprocess sequences can be terminated and backward coupling becomes possible. The system isconsolidated, the structure strengthened and adapted to the necessities. [For our blacksmith's forge this means that the market oriented processes and the processeswhich preserve or alter the system control one another mutually, i.e. that the new system forgeadjusts its production to its capacity or, vice versa, the investments in the new forge correspondto the necessities of the markets. The forge participates in the market, with regard both tomaterial procurement and to turnover. This necessitates compactness and causes it to take a formwhich permits these contacts.]

The example of the forge is located between the third and the forth level of complexity (cf.chapters 3 and 4). But these four phases of the emergence process can also be established as afixed principle for the other transitions from one type of system to the next. This formalprocedure makes it possible to follow and verify the processes of emergence (cf. Appendix).

Levels of complexity

Let us begin our considerations in the world of our experience, the Mesocosmos (Vollmer 1985,p. 57 f.), and proceed from the simple, i.e. the non-complex, to increasingly higher stages of "thecomplex". The process is at the center.

1. Solid body ("solidum") and movement (cf. Appendix, fig. 1)

The simplest process is the movement of an object, a "solidum". E.g. if a stone receives animpulse, it moves in a certain direction; it is then braked by an opposing force until it comes torest again. The impulse comes from outside, from the "superior environment". The opposing

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force also comes from outside, but this time from the "inferior environment". Here, we areassuming that the impulse to the solid object is not without consequence, but that the inferiorenvironment reacts in the same way as with an elastic impulse. The following example is takenfrom our everyday experience.

An object (solidum) is moved, e.g. a motion of the hand is executed. The following stages canbe observed, first of all starting from the superior environment:1. In the course of a superior planning or reaction of an individual (as the superior environment)a hand is stimulated to execute a movement;2. the stimulus is transferred to the body of the individual (inferior environment), to obtainenergy for the movement;3. the stimulus is received by the body of the individual;4. the stimulus is stopped.Thus, the process of stimulation from the superior environment comes to an end and the reactionof the inferior environment follows:1. the energy is released;2. the energy is transferred to the hand;3. the hand receives the energy;4. the hand executes the movement, the flow of energy ends in the superior environment. This process demonstrated here by a motion of the hand, can be used as an example of afundamental process, observed universally in reality. It forms the basis of all movements of solidbodies (solida) - because each beginning of a movement is accompanied by an end, and affectsthe environment more or less, regardless of whether the solida are hands, stones or cars.

2. Equilibrium system and movement projects (cf. Appendix, figs. 2 ... 5)

Let us assume that the motion of the hand is part of an ensemble of movements of solida forming(an action project or a movement project, e.g. the ploughing of a field or the writing of a book).Then many solida are moved in order to achieve the aim. We would then distinguish betweena whole, i.e. a system, and its parts, i.e. the individual elements. On an average each solid bodyand each movement, each arm and each motion of the hand contributes to the movement of thewhole system, but, on the other hand, is also subjected to that movement.

The movement projects with their ensembles of solida are - ideally - a simple system, anequilibrium system. The elements contribute to the movement of the whole and are in a stablestate of equilibrium. From an energetic point of view, the whole corresponds to the sum of theparts, if the movement is smooth, i.e. without vortexing. The elements adapt to the inferiorenvironment as source of energy. These systems are linear.

Each undifferentiated substance of this kind consisting of moveable parts, is an equilibriumsystem. This type of system also includes liquids, for instance standing or smoothly flowingwater where no energy (for instance much heat) is applied from outside. The molecules are theelements. Their space requirement depends on the energy content. They perform unaligned,haphazard movements (Brownian moleculare motion), the structure of the system itself,however, is not affected. Other examples are characteristic groups e.g. persons belonging to oneprofession as elements in an area, animals of one species in an area or piles of sand with grainsas elements.

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3. Flow equilibrium system and flow processes (cf. Appendix, figs. 6 ... 9)

The equilibrium system is not yet a complex structure. Complexity requires that at least 2substances or equilibrium systems with different energy contents interact with one another. Agroup of equilibrium systems resp. movement projects is stimulated by another group ofequilibrium systems and movement projects. The two groups do not have to mingle, butnevertheless it must be possible to transport energy from one of these systems to the other. Forthis purpose a transport medium is required, either the transport of (and trade with) goods inindustry, or a liquid which transfers heat or chemical energy, or radiation, electric power, etc.So these systems become compartments of a new type of system. The energy flows from onecompartment (the producer), to the other (the consumer). We call this flow process. Bothcompartiments together create a kind of internal market. A balance is sought. The producerssupply energy, the consumers demand energy. The demand is information, so that there is a flowof information from the consumer to the producer (demand), and a flow of energy from theproducer to the consumer (supply). We call this a flow equilibrium system.

Systems of this type distribute and control the flow of information and energy. Energy is lost inthe process (dissipation; Nicolis and Prigogine 1987). However, no conversion of energy takesplace (as in the non-equilibrium systems, cf. chapter 4).

In a closed flow equilibrium system, which receives no energy from outside, the energy flowdwindles to a stop. The result is an energetic equilibrium (cf. chapter 2). In an open system,however, which receives new energy, a flow equilibrium in which the system is able to retainits structure develops separately from the energetic equilibrium.

The separating of information and energy into their own process branches allows the system toregulate itself through feedback. This is possible, because each demand stimulates a flowprocess. If demand and supply do not correspond at the end of the process, the demand re-entersthe system. Now there are numerous systems in society and nature which do not at any timemanage to adapt the energy demand to the energy supply, because the energy supply is linkedwith the transport or even with the conversion (cf. chapter 4) of the energy demanded. Thiscauses a delayed reaction to the demand by the producer (and perhaps an over-reaction by theprocess, i.e. a temporary excess in supply). This causes oscillations and therefore the intermittenttransfer of energy; due to feedback, this in turn causes continuous readaptation by the system tothe demand. Consumer and producer stimulate one another continuously and so stabilize theirown existence. In these systems (in contrast to the equilibrium systems) the whole is more thanthe sum of its parts, i.e. they are nonlinear systems and can be termed complex.

Flow equilibrium systems are ubiquitous. One example is the above mentioned market, wherecertain goods are transferred from one side (i.e. the producer) to the other (the comsumer). Manyenergy flows of this kind form the basis for the economy of a region, where substances serve asraw materials for different levels of production. Demand and supply oppose one another andstrive to achieve a balance. Similarly, the ecosystems contain many "markets" of this kind. Theplants extract nutritive substances from the soil, and they themselves serve as food for animals.Here too, one may speak of producers (plants, suppliers) and consumers (animals, demanders;Ellenberg 1973). In both cases the aim is an (flow) equilibrium between demand and supply. Theeconomy or the ecosystem of a region is frequently studied in the same way as flow equilibriumsystems (for instance Forrester 1969). However, it should be remembered that the economic and

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ecosystems also include the production itself, so they possess a higher degree of complexity (cf.chapters 4 and 6).

Flow equilibrium systems are also characteristic of inorganic nature. Thus, the socalled chemicalclocks belong to this field (e.g. Nicolis and Prigogine 1987, pp. 29 f.; Hess and Markus 1986).Several substances interact in these systems, exchanging energy. In technology, a desired valueis frequently put into the system for the orientation of the process. Well known examples of thisare the speed controllers in steam engines or temperature controllers in heating systems.

4. Non-equilibrium system and conversion process (cf. Appendix, figs. 10 ... 13)

If the flow equilibrium system is overloaded for a long period of time (e.g. if more energy isdemanded than can be delivered), a state of chaos may arise. Before this happens, however, "atthe edge of the chaos", the system reacts with "emergence", i.e. pattern formation in whichcertain signs of self organization can be detected.

These processes are the subject of extensive research activity (socalled complexity research;Langton [ed.] 1989; Epstein and Axtell 1996). However, the step from the level of flowequilibrium systems to the level of permanent non-equilibrium systems cannot be attempted inthis way. Such permanent non-equilibrium systems may be, for example, biotic populations,organisms etc. ("artificial life") or social populations (companies, communities, states etc.;"artificial society"). They are part of a higher level of complexity.

Non-equilibrium systems have the ability to convert one kind of energy to another, for instancefrom chemical to kinetic energy, or from electrical to thermal energy, etc. In other words, non-equilibrium systems produce. Several flow equilibrium systems may unite to a non-equilibriumsystem to serve a certain purpose. As part of the division of labor, they assume tasks for a newwhole. Energy - as matter - is shaped into products, i.e. it is furnished with information so thatit exactly suits to the needs of the demanding consumer, who asks for it in the market and whois able to utilize exactly this energy form.

A further condition for the conversion of energy are processes which perform different tasks insuccession in accordance with certain rules. There are two part processes: induction and reactionprocess. In the induction process 4 information converting process stages appear first, followedby 4 energy converting process stages. The stages have certain tasks:1. "Perception": The non-equilibrium system receives the information as a stimulus from thesuperior demanding environment;2. "Determination": The non-equilibrium system decides for (or against) the acceptance of theinformation;3. "Regulation": The control between the system as a whole and the elements is regulated;4. "Organization" a: The system arranges the information flow to the inferior environmentspatially;5. "Organization" b: The system arranges the energy flow from the inferior environmentspatially; 6. "Dynamization": The energy is distributed to the elements;7. "Kinetization": The conversion of energy takes place by combining of the different individualenergies or material according to the information received;8. "Stabilization": The finished product is offered to the superior environment. In the product

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information and energy are stored and can be transmitted.

The organization stages (4 and 5) at the transition from the information converting to the energyconverting parts of the process overlap in time, so instead of 8, only 7 stages result.

The reaction process follows. It is performed in the same manner like the induction process, butleads into the system, changes it, adapts it to the new conditions by giving it a new structure orsize (or both). The performance of the process requires a spatial coherence of the systems, i.e.distinct limits, otherwise energy is wasted. So non-equilibrium systems organize themselves, i.e.their internal energy flows in such a way that as little energy as possible dissipates. The internalorganization is accompanied by a specific shape, into which the systems can develop (fororganisms: "equifinality"; v. Bertalanffy 1950, p. 25). So non-equilibrium systems are definableand can be typified. They strive continuously to secure or enlarge their sphere of influence, i.e.their energy resources.

Because the last stage of the induction process (stabilization) overlaps with the first stage of thereaction process (perception), the whole process consists not of 14 but only of 13 stages.

It is obvious that the process is irreversible. Energy is continuously required, not only totransform the structure or the size of the non-equilibrium system ("changing processes"), but alsoto maintain it ("conserving processes"). In the conserving processes, only as much energy isdemanded as the system needs for its own maintenance. Here the processes carrying out differenttasks run simultaneously, like the organs in an organism, or the departments in a company whichhave different tasks and interact continuously with one another. The organs or departments maybe considered as subsystems of the organism or the company, i.e. subordinate non-equilibriumsystems.

All the tasks have to be performed. However, not all stages are always clearly recognizable assuch. Many processes are incomplete, are broken off, and frequently two partial processes areperformed in one single stage.

The non-equilibrium systems are the actual centres of activity in our universe. Typical examplesare the organisms and organs, populations and industrial companies, molecules and atoms, starsand galaxies.

5. Hierarchy system and hierarchy process (cf. Appendix, figs. 14 ... 17)

The non-equilibrium systems deliver the demanded products to the superior markets, i.e. flowequilibrium systems, which distribute them. On the other hand the non-equilibrium systemsreceive the energy which they need for the conversion into products through subordinate flowequilibrium systems. This energy, again, is made available by subordinate non-equilibriumsystems, subsystems or elements. In this way a hierarchy becomes recognizable with differentlevels which themselves consist of a number of non-equilibrium systems. So the verticalinformation and energy flow is hierarchically ordered. These hierarchies enable a control of theproduction in the non-equilibrium systems over several levels. In this way, the inferiorenvironment is used to a great extent as a differentiated source of energy in order to use thematerials better in accordance with the differentiated requirements.

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The induction process performs the control. Each non-equilibrium system is reached. It has itsown specific task in the energy flow along with the other non-equilibrium systems of the samehierarchical level. It obeys the orders, because its existence depends on its integration in the flowof information and energy. So the information and energy (products) can be transmitted betweenthe demanding consumers and the supplying producers in exactly the form required. Selectionand evolution become possible, because each non-equilibrium system is adjacent to other non-equilibrium systems of the same kind which are in the same (i.e. competing) situation. Thereaction process stabilizes and arranges the whole hierarchy system. In doing so, new non-equilibrium systems are structurally (not materially; cf. chapter 6) created.

Empirical investigations (Fliedner 1981, 1997) permit the conclusion that the ubiquitouslydistributed human populations (i.e. the human society) arrange themselves into a hierarchy asnon-equilibrium systems (level): Mankind as a population (1), cultural populations (2), peoples and states (3), city-umland-populations (4), communities (5), families and companies (plants or small business holdings) (6),and individuals as elements (7). The hierarchical levels are held together by a vertical process,each level is characterized by its task and the "basic institutions" performing that task.

The tasks of the non-equilibrium systems at the individual levels (8, is actually 7, due tooverlapping; cf. chapter 4) of the hierarchy systems correspond to those which the non-equilibrium systems have to perform in their induction process. Thus, the sequence perception... stabilization is also recognizable in the vertical process. The duration of the processesdecreases from above to below. In each subordinate non-equilibrium system, the inductionprocesses have to be performed at least 7 times faster than in the superordinate systems, becausethe subordinate systems "work for" the superordinate systems. So the number of the subordinatenon-equilibrium systems increases positive exponentially down the hierarchy, whereas theduration of the process stages decreases negative exponentially down the hierarchy.

For example, the cultural populations (like Europe or the Orient) are responsible for the task ofdetermination (long term values; basic institutions magic, religion), the states and the peoplesare responsible for the task of the regulation (basic institution: rule in the wide sense, includingadministration). Possibly the living world can be hierarchically differentiated in a similar way:Living world as whole (1), empires (2), species (3), organisms (4), organs (5), cells (6), andorganic molecules as elements (7).

Most of the hierarchies, however, are structured incompletely, they consist of less than 7 levels.At the individual levels different tasks may be performed. Nevertheless, each non-equilibriumsystem is securely bound into a hierarchy and possesses a defined task for this hierarchy. In thehierarchical systems, non-equilibrium systems are created structurally.

6. Universal system and the universal process (cf. Appendix, figs. 18 ... 21)

At the next higher level of complexity on the other hand, the non-equilibrium systems are alsocreated materially. In a certain sense, the (physically defined) matter can be regarded asconsisting of non-equlibrium systems. Matter which is located outside the system serves as asource of energy and is consumed as a substance. The systems, i.e. forms, are created from these.The form of the system on the other hand makes possible the reception of substance. Thus, thenon-equilibrium systems are at the center as compact formations and intervene in the space

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outside themselves to obtain other matter as energy.

Demand and supply transfers, information and energy flows must be orientated in complexsystems and precisely connected with another. On the other hand, they must be screened fromeach other, so that they do not disturb each other and lose their distinctiveness by noise resp.dissipation. This is attained on the one hand by making the energy usable and transportable, i.e.by creation of matter as substance, and on the other hand by bringing distances into and aroundthe system, i.e. by creating space which is free from the substances of which the elements resp.the systems consist. The substances can be created only then, when their substantial ingredientsare extracted from the space. So substance and space are antagonists which are related to oneanother within the frame of systemic structures.

The global ecosystem (from a functional point of view) or the biosphere (from a spatial point ofview) we are familiar with may be taken as an example. It is the visible expression of the spatialcoexistence of living matter in the most varied forms. The information (demand) and energy(supply) flows demonstrate on the one hand the connection and on the other hand the isolationfrom each other, and this in a nearly perfect manner.

Each living creature seeks only very specific, exactly suited nutrition sources, and this creatureitself is also required as a nutrition source by only a few other creatures. Here the organisms, i.e.non-equilibrium systems, are themselves involved in the flow of energy, are snatched up anddestroyed, serve as substance for building up new life, new organisms. Every individual tries tobring the procurement of energy from outside into harmony with the transformation of energyin the interior. Thus, it controls its energy demand and supply itself, and utilizes the receivedenergy as effectively as possible.

The outer form and the internal spatial structure are of decisive importance. The living beingscreate their own forms. We are dealing with forms and spaces which are organized from inside.Maturana and Varela (1984, pp. 50 f.) described living beings as "autopoietic", self creatingsystems. As we know from research into evolution, the form of living organisms is the long termresult of adaptation to environmental conditions.

The spheres neighboring on the biosphere are affected in the process. We now leave the ordersof magnitude of the Mesocosmos. From the biosphere we arrive at the Macro- and Microcosmos.

On the one hand, the biosphere is embedded in the three large non biotic compartments on theearth, the rock formations, the water and the atmosphere, which we will call the "sphere of thechemical systems". On the other hand, the material composition leads to the development andthe decay of living beings right down to the "sphere of molecules". These two inorganic spheresare connected to one another, because the molecules compose the chemical systems. However,they are autonomous spheres with their own processes and systems. The non-equilibriumsystems of the sphere of molecules are the molecules. Those of the chemical sphere however arenot permanent formations, e.g. cyclones, eddies etc.

Like in the biosphere, the anorganic non-equilibrium systems consume other non-equilibriumsystems, to use the energy which is stored in their matter. They convert it and create new non-equilibrium systems. These in turn fall apart and give energy for new processes of formation.Thus, the systems at this complexity level are created not only structurally (cf. chapter 5) but also

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materially and spatially.

This also applies for the other spheres in the universe. Depending on the process sequence, thereare probably 16 of these in all (by overlapping 13; cf. chapter 4). As seen spatially they arearranged hierarchically around one another like the skins of an onion. The spheres form theenergetic interaction spaces with their own laws. Matter is formed by specific substances withquite different characteristics. This ensures that the processes perform their tasks for the universewithin their own orders of magnitude. In this way the processes within the molecules aredistinguished, for instance, from those within the ions or atoms. The levels to which thesesystems belong, are clearly distinguished from another, so that information and energy flows arescreened from another. Only in this way can the processes take place in a controlled manner.

The other forms, e.g. the quarks, the planetary systems or the galaxies may also be assigned tocertain spheres on the scale. This final chapter should actually be written by physicists, but whenthe literature accessible to non physicists is considered (e.g. Weinberg 1977; Hawking 1988;Landy 1999), one has the impression that these theoreticians occupied with the phenomenon inthe macrocosmos (e.g. theory of relativity) or the microcosmos (e.g. quantum theory) are mainlyconcerned with causality, but neglect finality, without which no research into complexity ispossible. What physicist enquires what functions the quarks, planetary systems or galaxies havein the code of systems and processes for the universe as a whole? Perhaps physics, which fordecades has had such an important influence on the social sciences, will now be able to learnfrom the social sciences in their research into our complex reality.

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References:

- von Bertalanffy, L.(1950): The Theory of Open Systems in Physics and Biology. In: Science,Vol. 111, pp. 23-29.- Ellenberg, H. (1973): Ökosystemforschung. Berlin, New York etc. (Springer) - Epstein, J. and R. Axtell (1996): Growing Artificial Societies. Social Science from the BottomUp. Washington, D.C. (Brooking Institution) and Cambridge, Mass. (MIT).- Fliedner, D. (1981): Society in Space and Time. = Arbeiten a. d. Geograph. Institut der Univ.des Saarlandes, 31. Saarbrücken. - Fliedner, D. (1993): Sozialgeographie. Berlin, New York (De Gruyter).- Fliedner, D. (1997): Die komplexe Natur der Gesellschaft. Systeme, Prozesse, Hierarchien.Frankfurt, Berlin, New York (Lang).- Fliedner, D. (1999): Komplexität und Emergenz in Gesellschaft und Natur. Typologie derSysteme und Prozesse. Frankfurt, Berlin, New York (Lang). To be publ.- Forrester, J.W. (1969): Urban Dynamics. Cambridge/Mass.(MIT).- Hawking, St.W. (1988): A Brief History of Time; From the Big Bang to Black Holes. NewYork (Bantam).- Hess, B. and M. Markus (1986): Chemische Uhren. In: Dress, A., H.Hendrichs and G. Küppers(eds.): Selbstorganisation. München, Zürich, pp. 61-79. - Landy, St.D. (1999): Die Struktur des Universums. In: Spektrum der Wissenschaft, Sep. 1999,pp. 42-48. - Langton, C.G., ed. (1989): Artificial Life. Redwood City, Cal. (Addison-Wesley). - Lissack, M.R. (1999): Complexity - the Science, its Vocabulary, and its Relation toOrganizations. In: Emergence 1.- Mainzer, K. (1994): Thinking in Complexity. The Complex Dynamics of Matter, Mind, andMankind. Berlin, Heidelberg etc. (Springer).- Maturana, H.R. and F.J. Varela (1984): Der Baum der Erkenntnis. Die biologischen Wurzelndes menschlichen Erkennens. (Transl. Span.). Bern, München (Scherz).- Nicolis, G. and I. Prigogine (1987): Die Erforschung des Komplexen. Auf dem Weg zu einemneuen Verständnis der Naturwissenschaften. München, Zürich.- Vollmer, V. (1985): Was können wir wissen? Vol. 1. Stuttgart. pp. 57-115. - Weinberg, St. (1977): The First Three Minutes. A Modern View of the Origin of the Universe.New York (Basic).

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Appendix: About the emergence processes

The stages between the levels of complexity are bridged by the emergence processes. This isdescribed briefly below in order to assist in understanding the typology of the systems andprocesses. As characteristics also emerge with every new stage of complexity, the processes aredescribed as emergence processes, although in the literature this term is only used for thetransition between flow and non-equilibrium systems (cf. appendix, chapters 3 and 4).

1. Solidum and movement

The following individual stages of movement can be identified (cf. fig. 1a):From the (superordinate or) superior environment:1. Impulse from the superior environment;2. the solidum is accelerated;3. immersion in the (subordinated or) inferior environment;4. receipt of the stimulus by the inferior environment.From the inferior environment:1. Inferior environment detects and forms itself;2. inferior environment gives solidum impulse;3. counter-force is absorbed in the solidum;4. solidum passes impulse on, accelerates into the superior environment.The inferior environment reacts according to ist consistency. Physically, this is equivalent to theelasticity of a base onto which a ball falls (elastic impulse).

Here the solidum is the main concern. It is directly affected by the process in stages 1 and 2 inthe sequence proceeding from the superior environment and in stages 3 and 4 in the sequenceproceeding from the inferior environment. On the other hand, stages 1 and 2 of the sequenceoriginating in the inferior environment and stages 3 and 4 of the sequence originating in thesuperior environment concern the inferior environment. In our process they are folded behindthe upper part. They belong to the moved solid but are not subject to the control of the solidum.We can formalize the movement of a solidum using a system of coordinates (cf. fig. 1 b):The stimulus is entered in the (+x,+y)-quadrant.The transfer of the stimulus to the inferior environment leads vertically downwards into the (+x,-y)-quadrant.The energy intake from the inferior environment takes place below the abscissa in the (-x,-y)-quadrant.The actual work performed by the movement then takes place in the (-x,+y)-quadrant. Thus, 2 polarizations are produced:- vertically, along the ordinate, the demand and the supply (of energy),- horizontally, along the abscissa, between the stimulus and the action, i.e. the sequence in time.

Within the system of coordinates, we can depict how the stimulus and the energy are receivedand how they are answered by the body. However, as we are concerned with the concept ofcomplexity, we are not interested in the performance of the movement in detail - i.e. for instancein the velocity which could be represented by a function - but only in the relationship betweenthese events. It is therefore sufficient to consider the coordinate systems themselves and theirquadrants.

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2. Equilibrium system and movement project:

In order to rise to the equilibrium system and the movement projects, 4 different operations arenecessary to characterize the emergence process correctly and completely (cf. figs. 2 .. 5):

1. Each single element (solidum and movement) can be represented by a system of coordinates.All the elements execute their movements as parts of a whole. The first operation can berepresented by an accumulation of coordinate systems (cf. fig. 2): "bundling".

2. The elements are assembled to form the new whole of the movement project ("alignment"; cf.fig. 3). Thus, it is necessary to distinguish two levels, the whole and the elements. The wholemust complete the movement, just as each part i.e. element. In the system as a whole, receptionof the stimulus from outside (1), the transfer of the stimulus to the entire project (2), theabsorption of the energy (3), and the execution (4) have to be taken into account. This can bedepicted by a comprehensive system of coordinates (1st rank) which symbolizes the basicstructure of the operations. The quadrants contain the partial processes:

(1) quadrant +x,+y,(2) quadrant +x,-y,(3) quadrant -x,-y, and(4) quadrant -x,+y.

In addition the elements with their own movements must be considered. As all of them aresubordinate to the system and involved in its movements, the movements are integrated in thewhole. This can be represented by 2nd rank coordinate systems. In average, the individualelements participate in the four movements of the main system (i.e. the movement or actionproject) symbolized in the quadrants of the overriding coordinate system. This can berepresented in such a way that the subordinate coordinate systems (2nd ranking systems) of theaverage single movements are inserted in each quadrant of the overriding (1st ranking) system.Depending on their position in this coordinate system the subordinate process stages 1-2-3-4 arereflected at the abscissa and the ordinate.

3. Now we are not only dealing with just a transfer of energy as in a motion of the hand i.e. asimple movement. Instead, the temporal sequence has gained in importance. The elements intheir own movements are connected with the system to form a process ("interlacement"). In ourtreatment of the solid body (cf. appendix, chapter 1), the movement was represented in thecoordinate system in a mathematically positive direction. If we wish to comprehend the wholesystem and the elements in their temporal sequence, we must align them horizontally. Thus thecoordinate systems have to be inverted.

This has to take place in two operations, as depicted in fig. 4 (interlacement).a) Firstly the numbers representing the individual stages of the movements in each of the four(2nd rank) coordinate systems of the elements have to change their places, i.e. on the diagonaly=x. Thenb) these values are again converted according to their position in one of the 4 quadrants of thesuperior (1st rank) coordinate system.

4. The last stage is the "folding" stage (cf. fig. 5) the coordinate systems are resolved. The

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horizontal process of the system (1st rank process) appears as a sequence of 4 stages 1-2-3-4. Asthe uppermost line shows, it takes place from right to left. The (2nd rank) element processes,however, are vertically ordered. The stabilization of the process is represented by the actualprocess of folding. The former y-negative quadrants (in fig. 5a these are shown offset slightlydownwards) are "folded" behind the former y-positive quadrants (cf. fig. 5c). Taken together, the stages described above - bundling, alignment, interlacement, folding - formthe emergence process. By structuring the coordinate systems at the system and element levels,symmetry (the structure) and asymmetry (the process) are brought into an order.

3. Flow equilibrium system and flow process:

The next step leads from the equilibrium system (movement project) to the flow equilibriumsystem (flow process). The emergence process shows us formally the way (cf. figs. 6 .. 9). Ittakes place according to the same pattern as with the equilibrium system.

The four stages of bundling, alignment, interlacement and folding are shown here for a betterunderstanding of the procedure used. The process sequence of the y-positive (front) part of thefolded equilibrium system (cf. appendix, chapter 2) forms the start and appears (according to thebundling stage (cf. fig. 6) in the alignment stage in the +x,+y quadrant of the system. In the otherquadrants, this sequence is reflected as with the equilibrium system (cf. fig. 7). In the subsequentinterlacement stage (cf. fig. 8), the procedure is also the same as that shown in the discussion ofthe equilibrium system, i.e.a) Reversal of the smallest process units, each of which includes 4 figures;b) Rearrangement of the figures in these process units according to the position in the 1st rankingcoordinate system;c) Reversal of the smallest process units consisting of 4 figures as a whole into the verticalposition, thus creating 2 new process units, each including 16 figures;d) Rearrangement of the figures in these new units according to the position in the halves of the1st ranking coordinate system. Through folding at a horizontal hinge (cf. fig. 9) these processes are connected to one anotherto produce circular processes. Geometrically this produces a pipe shaped structure. As a resultof this transformation process 4 superimposed levels appear (bonding levels). In each of theseslevels 2nd rank process stages are present.

The 1st rank process running through the whole system, is vertically aligned. The information(demand) from the superior environment is directed downwards, whereas the energy (supply)from the inferior environment is directed upwards. So the same structures, i.e. the four bondinglevels are gone through one after another in the opposite direction. The sequences of the partprocesses 1-2-3-4 are connected with one another back to back (1-2-3-4/4-3-2-1).The 2nd rank processes (movement projects) run in a horizontal direction. The structure of thistype of process can be seen in the diagram.

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4. Non-equilibrium system and conversion process:

As already underlined, the flow equilibrium systems must be distinguished from the non-equilibrium systems. The transition ist again described by the emergence process.

The three first stages of the emergence process are bundling, alignment, and interlacement (cf.figs. 10 .. 12). They can easily be visualized using the rules given in (appendix) chapters 2 and3. In the folding process (fig. 13) 8 links of the induction process appear horizontally from rightto left, along with 8 links of the reaction process in the same direction. In each stage of this 1strank process, the 4 bonding levels (cf. appendix, chapter 3) have to be vertically opened up by2nd rank processes. These 2nd rank processes (the flow processes) run in a vertical direction.(The structure of this type of process can be seen in the diagram).

In the horizontal process, the individual vertical processes which correspond to the processes inthe flow equilibrium systems, are put together to form a new whole. The induction and reactionprocesses have to be coupled to one another at their ends and beginnings, thus forming a circularprocess. So geometrically they form a torus shaped structure. It symbolizes a 1st rank horizontalcircular process, to which 2nd rank circular processes contribute.

The induction process is oriented towards the demanding superior environment. The informationis conducted down the bonding levels (perception ... organization) and the energy up the bondinglevels (organization ... stabilization). Thus, the same bonding levels are gone through from twosides. The formulae described for the part processes thus appear twice, in reverse order to oneanother, back to back, so to speak (1-2-3-4/4-3-2-1).

5. Hierarchical system and hierarchical process:

In accordance with the above-mentioned pattern (cf. appendix, chapters 2 and 3), the complexionprocess (cf. fig. 14 .. 17) leads to the next complexity level. As the result of the folding (cf. fig.17) 8 levels can be seen at which the (horizontal) processes in the non-equilibrium systems aretaken place and are joined to form circular processes (cf. appendix, chapter 4). These 2nd rankprocesses in the non-equilibrium systems of the several hierarchical levels are bracketed by a 1strank vertical process. The induction process runs in a downward direction, i.e. from the wholevia the subsystems to the elements, and the reaction process from the elements up to the wholeof the hierarchy as the uppermost level. So induction and reaction processes are connected withanother back to back (1-2-3-4-4-3-2-1/1-2-3-4-4-3-2-1).

Die 2nd rank processes (conversion processes) run in a horizontal direction. (The structure ofthis type of process can be seen in the diagram.)

6. Universal system and universal process:

With the assistance of the emergence process we can progress to the next complexity level. Thepattern explained above (cf. appendix, chapter 2) with its 4 stages (bundling, alignment,interlacement, and folding; cf. figs. 18 .. 21) is also the basis of this process. As the result offolding, a horizontal sequence of 16 tasks of the 1st rank induction process is recognizable. Theymust be solved, so that the whole remains conserved or can be changed. The induction process

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runs from right to left, followed by the reaction process which has to be coupled to the inductionprocess. The single tasks are performed by subordinate (2nd rank) vertical processes, each ofwhich consists of 8 links. These 2nd rank processes (hierarchical processes) run in a verticaldirection. (The structure of this type of process can be seen in the diagram.) By folding (cf. fig. 21) the reaction process is turned behind the induction process. Soappropriate 2nd rank processes are connected in circular processes with 16 links each.

Figures: b) Superior Environment a) 4 1 3 2 4 1 2 3 3 2 1 4 Inferior Environment Fig. 1: Scheme of the course of a movement.a) The vertical arrangement of the stages between solidum and inferior environment;b) The stages of movement assigned to the solidum. The stages concerning the inferiorenvironment are folded behind. The stages of movement assigned to the solidum can be depictedin the quadrants of a coordinate system. The numbers symbolize the sequence (in clockwisedirection). (The axes of the coordinate system are not shown.)

i=n ∑ 4 1 i=1 3 2 Fig. 2: Scheme of the movement project in the bundling stage. Compare with fig. 1. Themovement project incorporates n movements. The 4 individual stages of a movement are shown,the numbers represent the process sequence.

1 4 4 1 2 3 3 2 2 3 3 2 1 4 4 1

Fig. 3: Scheme of the movement project in the alignment stage. Compare with fig. 2. Thebundled movements are divided into 4 groups for the new process. A new (1st rank) coordinatesystem is set up. In each quadrant, 2nd rank individual coordinate systems appear for the bundledmovements. (The axes of the coordinate systems are not shown.)

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a) 3 4 2 1 b) 4 3 2 1 2 1 3 4 1 2 3 4

4 3 1 2 2 1 4 3 1 2 4 3 3 4 1 2

Fig. 4: Scheme of the movement projects in the interlacement phase. Compare with fig. 3. Thevertically aligned sequence is arranged horizontally. The reversion operations are shown. (Theaxes of the coordinate systems are not shown.)a) Reversion of the smallest quadratic process units, each containing 4 numbers;b) Rearrangement of the numbers in these process units according to the position in the 1st rankcoordinate system.

a) 4 3 2 1 1 2 3 4

2 1 4 3 3 4 1 2 b) 4 3 2 1 1 4 3 2 2 1 4 3 3 2 1 4 1 2 3 4 2 3 4 1 3 4 1 2 4 1 2 3 2 1 4 3 3 2 1 4 4 3 2 1 1 4 3 2 3 4 1 2 4 1 2 3 1 2 3 4 2 3 4 1 t 1 t 2 t 3 t 4 c) 4 3 2 1 1 2 3 4

Fig. 5: Scheme of the movement project in the folding phase. Compare with fig. 4. a) The coordinate system is removed. A movement project scheme is created.b) The diagram shows 4 stages (t1 ... t4) in the development of the equilibrium system resp.movement project. The 1st rank process proceeds from right to left. The 2nd rank processes areshifted in the corresponding pattern without changing their basic structure. They symbolize thesum of the solida or movements each with their 4 stages.c) The folding process is now carried out. The lower part is placed on the left beside the upperpart and then folded behind the induction process on an imaginary vertical hinge. The arrowshows the direction of the 1st rank process. Depiction of front section of process.

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i=n ∑ 4 3 2 1 i=1 1 2 3 4

Fig. 6: Scheme of the flow process in the bundling stage. Compare with fig. 5. The flow processincorporates n movement projects. The individual stages of a movement project are shown, thenumbers represent the process sequence.

1 2 3 4 4 3 2 1 4 3 2 1 1 2 3 4 4 3 2 1 1 2 3 4 1 2 3 4 4 3 2 1

Fig. 7: Scheme of the flow process in the alignment stage. Compare with fig. 6. The bundledmovement projects are divided into 4 groups for the new process. A new (1st rank) coordinatesystem is set up. In each quadrant, 2nd rank individual coordinate systems appear for the bundledmovement projects. (The axes of the coordinate systems are not shown.)

c) 2 3 4 1 d) 2 3 4 1 1 4 3 2 1 4 3 2a) 3 2 1 4 2 3 4 1 b) 2 3 4 1 2 3 4 1 4 1 2 3 4 1 2 3 4 1 2 3 1 4 3 2 1 4 3 2 1 4 3 2 3 2 1 4 3 2 1 4 2 3 4 1 3 2 1 4 4 1 2 3 4 1 2 3 2 3 4 1 3 2 1 4 1 4 3 2 4 1 2 3 3 2 1 4 3 2 1 4 1 4 3 2 4 1 2 3 4 1 2 3 1 4 3 2 3 2 1 4 2 3 4 1 Fig. 8: Scheme of the flow process in the interlacement phase. Compare with fig. 7. Thehorizontally aligned sequence is arranged vertically. The reversion operations are shown. (Theaxes of the coordinate systems are not shown.)a) Reversion of the smallest quadratic process units, each containing 4 numbers;b) Rearrangement of the numbers in these process units according to the position in the 1st rankcoordinate system;c) Reversion of the smallest process units (each containing 4 numbers) as wholes into the verticalposition. This shows the vertical process (flow of information above and flow of energy belowthe abscisse);d) 2 new quadratic units each with 16 numbers have been created. The lower, in the y-negativezone must be turned around on an imaginary horizontal axis.

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a) 2 3 4 1 1. Bonding level 1 4 3 2 2. Bonding level Information 4 1 2 3 3. Bonding level flow 3 2 1 4 4. Bonding level

3 2 1 4 4. Bonding level 4 1 2 3 3. Bonding level Energy 1 4 3 2 2. Bonding level flow 2 3 4 1 1. Bonding level b) 2 3 4 1 1. Bonding level 1 4 3 2 2. Bonding level Information 4 1 2 3 3. Bonding level flow 3 2 1 4 4. Bonding level

Fig. 9: Scheme of the flow process in the folding phase. Compare with fig. 8. a) The coordinate system is removed. A flow process scheme is created. The bonding levelsappear.b) The folding process is now carried out. The (above shown) information flow is folded behindthe (below shown) energy flow on an imaginary horizontal hinge. The arrows indicate thedirection of the 1st rank process (downwards for the information flow, upwards for the energyflow). Depiction of front section of process (information flow).

2 3 4 1 i = n 1 4 3 2 ∑ 4 1 2 3 i = 1 3 2 1 4

Fig. 10: Scheme of the conversion process in the bundling stage. Compare with fig. 9. Theconversion process incorporates n flow processes. The individual stages of a flow process areshown, the numbers represent the process sequence.

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1 4 3 2 2 3 4 1 2 3 4 1 1 4 3 2 3 2 1 4 4 1 2 3 4 1 2 3 3 2 1 4 4 1 2 3 3 2 1 4 3 2 1 4 4 1 2 3 2 3 4 1 1 4 3 2 1 4 3 2 2 3 4 1

Fig. 11: Scheme of the conversion process in the alignment stage. Compare with fig. 10. Thebundled flow processes are divided into 4 groups for the new process. A new (1st rank)coordinate system is set up. In each quadrant, 2nd rank individual coordinate systems appear forthe bundled flow processes. The arrows indicate the direction of the 1st rank process (clockwisedirection). (The axes of the coordinate systems are not shown.)

a) b) 1 4 3 2 2 3 4 1 1 2 3 4 4 3 2 1 2 3 4 1 1 4 3 2 4 3 2 1 1 2 3 4 3 2 1 4 4 1 2 3 3 4 1 2 2 1 4 3 4 1 2 3 3 2 1 4 2 1 4 3 3 4 1 2

4 1 2 3 3 2 1 4 2 1 4 3 3 4 1 2 3 2 1 4 4 1 2 3 3 4 1 2 2 1 4 3 2 3 4 1 1 4 3 2 4 3 2 1 1 2 3 4 1 4 3 2 2 3 4 1 1 2 3 4 4 3 2 1

Fig. 12: Scheme of the conversion process in the interlacement stage. Compare fig. 11. Thevertically aligned sequence is arranged horizontally. The reversion operation incorporating theentire table of numbers in the coordinate system is shown. (The axes of the coordinate systemsare not shown.)

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a) Sta Kin Dyn Org Org Reg Det Per 1 2 3 4 4 3 2 1 4 3 2 1 1 2 3 4 Induction- 3 4 1 2 2 1 4 3 process 2 1 4 3 3 4 1 2

2 1 4 3 3 4 1 2 3 4 1 2 2 1 4 3 Reaction- 4 3 2 1 1 2 3 4 process 1 2 3 4 4 3 2 1 Sta Kin Dyn Org Org Reg Det Per

b) Sta Kin Dyn Org Org Reg Det Per 1 2 3 4 4 3 2 1 4 3 2 1 1 2 3 4 Induction 3 4 1 2 2 1 4 3 process 2 1 4 3 3 4 1 2

Fig. 13: Scheme of the conversion process in the folding phase. Compare with fig. 12. a) The coordinate system is removed. A conversion process scheme is created. The processsequence and the tasks appear.b) The folding process is now carried out. The reaction process is placed on the left beside theinduction process and then folded behind the induction process on an imaginary vertical hinge.The arrows show the direction of the 1st rank process (in the induction process to left, in thereaction process to the right). Depiction of front section of process (induction process). Abbreviations:Per = Perception, Det = Determination, Reg = Regulation, Org = Organization, Dyn =Dynamization, Kin = Kinetization, Sta = Stabilization.

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1 2 3 4 4 3 2 1 i = n 4 3 2 1 1 2 3 4 ∑ 3 4 1 2 2 1 4 3 i = 1 2 1 4 3 3 4 1 2

Fig. 14: Scheme of the hierarchical process in the bundling stage. Compare with fig. 13. Thehierarchical process incorporates n conversion processes. The individual stages of a conversionprocess are shown, the numbers represent the process sequence.

1 2 3 4 4 3 2 1 1 2 3 4 4 3 2 1 4 3 2 1 1 2 3 4 4 3 2 1 1 2 3 4 3 4 1 2 2 1 4 3 3 4 1 2 2 1 4 3 2 1 4 3 3 4 1 2 2 1 4 3 3 4 1 2

2 1 4 3 3 4 1 2 2 1 4 3 3 4 1 2 3 4 1 2 2 1 4 3 3 4 1 2 2 1 4 3 4 3 2 1 1 2 3 4 4 3 2 1 1 2 3 4 1 2 3 4 4 3 2 1 1 2 3 4 4 3 2 1 Fig. 15: Scheme of the hierarchic process in the alignment stage. Compare with fig. 14. Thebundled conversion processes are divided into 4 groups for the new process. A new (1st rank)coordinate system is set up. In each quadrant, 2nd rank individual coordinate systems appear forthe bundled conversion processes. The arrows indicate the direction of the 1st rank process(anticlockwise direction). (The axes of the coordinate systems are not shown.)

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a) 3 2 1 4 2 3 4 1 3 2 1 4 2 3 4 1 b) 1 4 3 2 2 3 4 1 4 1 2 3 1 4 3 2 4 1 2 3 1 4 3 2 2 3 4 1 1 4 3 2 1 4 3 2 4 1 2 3 1 4 3 2 4 1 2 3 3 2 1 4 4 1 2 3 2 3 4 1 3 2 1 4 2 3 4 1 3 2 1 4 4 1 2 3 3 2 1 4 4 1 2 3 3 2 1 4 4 1 2 3 1 4 3 2 4 1 2 3 1 4 3 2 3 2 1 4 4 1 2 3 3 2 1 4 2 3 4 1 3 2 1 4 2 3 4 1 2 3 4 1 1 4 3 2 2 3 4 1 3 2 1 4 2 3 4 1 3 2 1 4 1 4 3 2 2 3 4 1 1 4 3 2 4 1 2 3 1 4 3 2 4 1 2 3 1 4 3 2 2 3 4 1 2 3 4 1 1 4 3 2 3 2 1 4 4 1 2 3 4 1 2 3 3 2 1 4 4 1 2 3 3 2 1 4 3 2 1 4 4 1 2 3 2 3 4 1 1 4 3 2 1 4 3 2 2 3 4 1

Fig. 16: Scheme of the hierarchical process in the interlacement phase. Compare with fig. 15.The horizontally aligned sequence is arranged vertically. The reversion operations are shown.(The axes of the coordinate systems are not shown.)a) Reversion of the quadratic process units, each containing 16 numbers;b) Reversion of the process units (each containing 16 numbers) as wholes from the horizontalinto the vertical position;(c) 2 new quadratic units each with 64 numbers have been created. The lower, in the y-negativezone must be turned around on an imaginary horizontal axis. This is not apparent because of thesymmetrical arrangement in this block.

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a) 1 4 3 2 2 3 4 1 Per 2 3 4 1 1 4 3 2 Det 3 2 1 4 4 1 2 3 Reg 4 1 2 3 3 2 1 4 Org Induction- 4 1 2 3 3 2 1 4 Org process 3 2 1 4 4 1 2 3 Dyn 2 3 4 1 1 4 3 2 Kin 1 4 3 2 2 3 4 1 Sta

1 4 3 2 2 3 4 1 Per 2 3 4 1 1 4 3 2 Det 3 2 1 4 4 1 2 3 Reg 4 1 2 3 3 2 1 4 Org Reaction- 4 1 2 3 3 2 1 4 Org process 3 2 1 4 4 1 2 3 Dyn 2 3 4 1 1 4 3 2 Kin 1 4 3 2 2 3 4 1 Sta

b) 1 4 3 2 2 3 4 1 Per 2 3 4 1 4 1 2 3 Det 3 2 1 4 4 1 2 3 Reg 4 1 2 3 3 2 1 4 Org Induction- 4 1 2 3 3 2 1 4 Org process 3 2 1 4 4 1 2 3 Dyn 2 3 4 1 1 4 3 2 Kin 1 4 3 2 2 3 4 1 Sta

Fig. 17: Scheme of the hierarchic process in the folding phase. Compare with fig. 16. a) The coordinate system is removed. A hierarchic process scheme is created. The hierarchiclevels (and tasks) appear.b) The folding process is now carried out. The reaction process is folded behind the inductionprocess on an imaginary horizontal hinge. The arrows indicate the direction of the 1st rankprocess (downwards for the induction process, upwards for the reaction process). Depiction offront section of process (induction process). Abbreviations:Per = Perception, Det = Determination, Reg = Regulation, Org = Organization, Dyn =Dynamization, Kin = Kinetization, Sta = Stabilization.

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1 4 3 2 2 3 4 1 2 3 4 1 1 4 3 2 3 2 1 4 4 1 2 3 i = n 4 1 2 3 3 2 1 4 ∑ 4 1 2 3 3 2 1 4 i = 1 3 2 1 4 4 1 2 3 2 3 4 1 1 4 3 2 1 4 3 2 2 3 4 1

Fig. 18: Scheme of the universal process in the bundling stage. Compare with fig. 17. Theuniversal process incorporates n hierarchic processes. The individual stages of a hierarchicprocess are shown, the numbers represent the process sequence. 1 4 3 2 2 3 4 1 1 4 3 2 2 3 4 1 2 3 4 1 1 4 3 2 2 3 4 1 1 4 3 2 3 2 1 4 4 1 2 3 3 2 1 4 4 1 2 3 4 1 2 3 3 2 1 4 4 1 2 3 3 2 1 4 4 1 2 3 3 2 1 4 4 1 2 3 3 2 1 4 3 2 1 4 4 1 2 3 3 2 1 4 4 1 2 3 2 3 4 1 1 4 3 2 2 3 4 1 1 4 3 2 1 4 3 2 2 3 4 1 1 4 3 2 2 3 4 1 1 4 3 2 2 3 4 1 1 4 3 2 2 3 4 1 2 3 4 1 1 4 3 2 2 3 4 1 1 4 3 2 3 2 1 4 4 1 2 3 3 2 1 4 4 1 2 3 4 1 2 3 3 2 1 4 4 1 2 3 3 2 1 4 4 1 2 3 3 2 1 4 4 1 2 3 3 2 1 4 3 2 1 4 4 1 2 3 3 2 1 4 4 1 2 3 2 3 4 1 1 4 3 2 2 3 4 1 1 4 3 2 1 4 3 2 2 3 4 1 1 4 3 2 2 3 4 1

Fig. 19: Scheme of the universal process in the alignment stage. Compare with fig. 18. Thebundled hierarchical processes are divided into 4 groups for the new process. A new (1st rank)coordinate system is set up. In each quadrant, 2nd rank individual coordinate systems appear forthe bundled hierarchical processes. The arrows indicate the direction of the 1st rank process(clockwise direction). (The axes of the coordinate systems are not shown.)

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a) b) 1 4 3 2 2 3 4 1 1 4 3 2 2 3 4 1 1 2 3 4 4 3 2 1 1 2 3 4 4 3 2 1 2 3 4 1 1 4 3 2 2 3 4 1 1 4 3 2 4 3 2 1 1 2 3 4 4 3 2 1 1 2 3 4 3 2 1 4 4 1 2 3 3 2 1 4 4 1 2 3 3 4 1 2 2 1 4 3 3 4 1 2 2 1 4 3 4 1 2 3 3 2 1 4 4 1 2 3 3 2 1 4 2 1 4 3 3 4 1 2 2 1 4 3 3 4 1 2 4 1 2 3 3 2 1 4 4 1 2 3 3 2 1 4 2 1 4 3 3 4 1 2 2 1 4 3 3 4 1 2 3 2 1 4 4 1 2 3 3 2 1 4 4 1 2 3 3 4 1 2 2 1 4 3 3 4 1 2 2 1 4 3 2 3 4 1 1 4 3 2 2 3 4 1 1 4 3 2 4 3 2 1 1 2 3 4 4 3 2 1 1 2 3 4 1 4 3 2 2 3 4 1 1 4 3 2 2 3 4 1 1 2 3 4 4 3 2 1 1 2 3 4 4 3 2 1 1 4 3 2 2 3 4 1 1 4 3 2 2 3 4 1 1 2 3 4 4 3 2 1 1 2 3 4 4 3 2 1 2 3 4 1 1 4 3 2 2 3 4 1 1 4 3 2 4 3 2 1 1 2 3 4 4 3 2 1 1 2 3 4 3 2 1 4 4 1 2 3 3 2 1 4 4 1 2 3 3 4 1 2 2 1 4 3 3 4 1 2 2 1 4 3 4 1 2 3 3 2 1 4 4 1 2 3 3 2 1 4 2 1 4 3 3 4 1 2 2 1 4 3 3 4 1 2 4 1 2 3 3 2 1 4 4 1 2 3 3 2 1 4 2 1 4 3 3 4 1 2 2 1 4 3 3 4 1 2 3 2 1 4 4 1 2 3 3 2 1 4 4 1 2 3 3 4 1 2 2 1 4 3 3 4 1 2 2 1 4 3 2 3 4 1 1 4 3 2 2 3 4 1 1 4 3 2 4 3 2 1 1 2 3 4 4 3 2 1 1 2 3 4 1 4 3 2 2 3 4 1 1 4 3 2 2 3 4 1 1 2 3 4 4 3 2 1 1 2 3 4 4 3 2 1

Fig. 20: Scheme of the universal process in the interlacement stage. Compare fig. 19. Thevertically aligned sequence is arranged horizontally. The reversion operation incorporating theentire table of numbers in the coordinate system is shown. (The axes of the coordinate systemsare not shown.)

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a) Microcosmos Macrocosmos1 2 3 4 4 3 2 1 1 2 3 4 4 3 2 14 3 2 1 1 2 3 4 4 3 2 1 1 2 3 43 4 1 2 2 1 4 3 3 4 1 2 2 1 4 32 1 4 3 3 4 1 2 2 1 4 3 3 4 1 2 Induction-2 1 4 3 3 4 1 2 2 1 4 3 3 4 1 2 process3 4 1 2 2 1 4 3 3 4 1 2 2 1 4 34 3 2 1 1 2 3 4 4 3 2 1 1 2 3 4 1 2 3 4 4 3 2 1 1 2 3 4 4 3 2 1

1 2 3 4 4 3 2 1 1 2 3 4 4 3 2 14 3 2 1 1 2 3 4 4 3 2 1 1 2 3 43 4 1 2 2 1 4 3 3 4 1 2 2 1 4 32 1 4 3 3 4 1 2 2 1 4 3 3 4 1 2 Reaction-2 1 4 3 3 4 1 2 2 1 4 3 3 4 1 2 process3 4 1 2 2 1 4 3 3 4 1 2 2 1 4 34 3 2 1 1 2 3 4 4 3 2 1 1 2 3 41 2 3 4 4 3 2 1 1 2 3 4 4 3 2 1Macrocosmos Microcosmos

b) Microcosmos Macrocosmos 1 2 3 4 4 3 2 1 1 2 3 4 4 3 2 1 4 3 2 1 1 2 3 4 4 3 2 1 1 2 3 4 3 4 1 2 2 1 4 3 3 4 1 2 2 1 4 3 2 1 4 3 3 4 1 2 2 1 4 3 3 4 1 2 2 1 4 3 3 4 1 2 2 1 4 3 3 4 1 2 3 4 1 2 2 1 4 3 3 4 1 2 2 1 4 3 4 3 2 1 1 2 3 4 4 3 2 1 1 2 3 4 1 2 3 4 4 3 2 1 1 2 3 4 4 3 2 1 ----------------------------------------------------------------------------------------------------------------Sta Kin Dyn Org Org Reg Det Per Sta Kin Dyn Org Org Reg Det Per Tasks 16 15 14 13 12 11 10 9 8 7 6 5 4 3 2 1 Spheres Mol Bio Chem

Fig. 21: Scheme of the universal process in the folding phase. Compare with fig. 20. a) The coordinate system is removed. A universal process scheme is created. b) The folding process is now carried out. The reaction process is placed on the left beside theinduction process and then folded behind the induction process on an imaginary vertical hinge.The arrows show the direction of the 1st rank process (in the induction process to left, in thereaction process to the right). Depiction of front section (induction process). Abbreviations: Per = Perception, Det = Determination, Reg = Regulation, Org = Organization,Dyn = Dynamization, Kin = Kinetization, Sta = Stabilization.